Point spread function modeling and engineering in black-box lens systems

Point spread function (PSF) engineering in an imaging system involves the introduction of additional optical components to efficiently encode object information. It typically relies on a well-established mapping relation between object space, PSF engineering plane, and image plane. However, this reliance can limit its application in imaging systems with unknown ("black box") attributes, e. g. commercial photographic lenses, where a theoretical imaging model is not readily available. To address this limitation, we conduct wave-optics analysis of general lens systems, explicitly derive a general imaging model based on scaled Fourier transform, and develop an overall pipeline for automatic parameter determination of the model. When applied to a photographic lens, this pipeline demonstrates high PSF modeling accuracy, showcasing the capability of "seeing what you design". We then implemented PSF engineering in this lens to find its optimal PSF for 3D localization. This work improves computational imaging by enabling accurate wavefront shaping design in arbitrary imaging systems.